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Fungrim entry: 888581

B ⁣(a,b)=Γ ⁣(a)Γ ⁣(b)Γ ⁣(a+b)\mathrm{B}\!\left(a, b\right) = \frac{\Gamma\!\left(a\right) \Gamma\!\left(b\right)}{\Gamma\!\left(a + b\right)}
Assumptions:aC{0,1,}andbC{0,1,}a \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\}
\mathrm{B}\!\left(a, b\right) = \frac{\Gamma\!\left(a\right) \Gamma\!\left(b\right)}{\Gamma\!\left(a + b\right)}

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\}
Fungrim symbol Notation Short description
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(BetaFunction(a, b), Div(Mul(GammaFunction(a), GammaFunction(b)), GammaFunction(Add(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC